How can I solve this non-linear ODE exactly or approximately in some series solution?

Non_linear_ode.mw

I'm a new Maple user so there may be a better way to do this, but Maple is not handling units the way I would expect.

Here is an example document (inline graphical below, also here: Plots_With_Units.mw) showing the impedance of a parallel resistor, inductor, and capacitor.  The plot is correct and it shows kHz along the abscissa like I want.  In order to get this I used kHz in the range fr, which is fine, but I had to also use kHz in the basic definition functions for Zl and Zc.

Now in order to get correct results from any of the Z functions I must use them with a kHz argument for f.  If I want to use them where other unit multipliers are more appropriate they won't work right, and many times I don't know what the appropriate multiplier should be until I'm into the design.  Then I need to go back and change the multipliers in the functions.  Or maybe in a single design I'll want to show Hz and kHz for the same function.

This seems like confusing units and dimensions.  The dimensions of inductive impedance (Zl), for example, can be expressed as frequency times inductance.  Whether the frequency is in units of Hz, kHz, or uHz doesn't matter and should simply scale the results.  I should be able to specify functions in dimensions and use units elsewhere as I want for convenient plotting and result formatting.

Is there a better way to do this, or is it a limitation in Maple?  The overall goal is to define functions with units but be able to use them and to format plots in whatever other units I like.

Hi,

I am trying to solve a 2nd order ODE. But I get the Error:

Error, (in dsolve/numeric/bvp/convertsys) unable to convert to an explicit first-order system

I have uploaded the worksheet. Can anybody please help me?

I am teaching a course in biofluid mechanics and am looking to help the students get more use out of Maple. Often it is advantageous to scale a differential equation (and initial conditions) using dimensionless variables to reduce the number of free parameters in a problem. For example, the simple linear oscillator differential equation:

Eq(1)         m*d²x(t)/dt² + k*x(t)=0

where k and m are parameters.  If we define a dimensionless time, s=t/T, and a dimensionless position, X=x/L, where T and L are constants, , Eq(1) becomes

Eq(2)         (mL/T² ) *d²X(s)/ds² +  kL*X(s)=0

Then choosing T=sqrt(m/k) we arrive at

Eq(3)         d²X(s)/ds² +  X(s)=0

which has no parameters.  Can this sequence be done in Maple for a differential equation...i.e. change of variables?

Thanks

I recently moved to a new research institute and have to make a decision on either buy a licence for Maple or Mathematica. My needs are PDE hyperbolic system (e.g. shallow water, tsunami...) resolution and when possible export to standalone C/Fortran code based on package like MathPDE.

I know a little of Mathematica, but have a bunch of notebooks. I tried with the help of MapleSoft support to import them into Maple with no success so far.

So as I'm not tied to any of both, I have the impression that I would be more comfy with Mma but Maple is cheaper and seems more open. Is there any rationals for picking one over the other?

I have a difficult problem by NLPSolve & mnimize (optimization)

How do I solve the erroe"unexpected parameters" in Maple?

The code is uploade under the line.
Maple Worksheet - Error

Failed to load the worksheet /maplenet/convert/example1.mw .

Download example1.mw

For most expressions e, op(0,e) gives the type, e.g. this works if e is of type string, list, set, Array, Vector, Matrix, '+', etc. This is not the case for procedure calls and indexed expressions, but these differences make sense. However, there are other puzzling differences, at least in Maple 2017.2, for which I can see no rationale.

Specifically, if e is a numeric type such as integer, float, or fraction, complex, then op(0,e) returns the capitalized version of the type, e.g. Integer. Note also that type(e,Integer) will generate an error message saying that type 'Integer' does not exist.

A Google search shows that in an old programming guide for Maple (Release V, p.135; copyright 1998), op(0,x) is "integer" if x is an integer, whereas in a more recent programming guide (the 2009 introductory one, p.53), it is capitalized, consistent with the behaviour in Maple 2017.

I do not understand why this change was made. Can anybody shed light on the situation?

hello

How I can remove these errors?

Thanks

erorr.mw
 

Download erorr.mw

How do I take the square root of :

    X:= r² (R + r cos(v))²

with the condition that R and r are positive and R>r and get:

r (R+ r cos(v))

I assume I need to use simplify with some assumptions, but I cannot figure it out.  

browsing on math.stackexchange I came across this maple code:

asympt(int(sqrt(-k^2+1)*exp(I*k*x), k = -1 .. 1), x, 2)

that gave the correct answer:

https://math.stackexchange.com/questions/532394/how-to-analyze-the-asymptotic-behaviour-of-this-integral-function

so I wondered would it not be great if maple done asymptotic expansion of integrals in general.

say as an example Li(x).  Can maple expand Li(x) and how?

I am perplexed about the geometry and plots packages.  When starting a programme involving geometric shapes, how does one decide which to use?  ..Or can the two packages be used in the same programme?  To iiiustrate my question there is a text program below which draws a diagram of a large square, with a circle inscribed tangentially to the square.  There is then a further smaller concentric circle, with a square drawn inside; the vertices touching this circle.  (It isdesigned as a problem suitable for young high-school teenagers.)

   I wanted to fill in various regions of this diagram in colors red and green.  I believe the with(geometry) package does this easily.  However, as I'm more used to the with(plots) package I stuck to this.  To get the coloured regions I drew a sequence of colored lines.  I also drew a colored square (See    SmallSq:=[op(SmallSq),sq_small||ii]:   ) by drawing a seq of concentric squares.  At the end of my program there are two almost identical plots[display] commands.   The difference is that the first does not incude the SmallSq.  I was expecting the two displays to be identical, since I'd specified the color white.  The first display has a dark colored square.  Why?? .  

   .   The program is very klutsy!  I'm embarrassed to publish it:-(  The SmallSq is adequate for my purposes, but has several white spaces - almost dots - on the dark version.  The thickness and style of the lines was the widest possible  - perhaps I should have set the larger rarius R, to a bigger value?

   And I have a feeling this diagram could have been constructed ib the geometry package in far fewer lines of code!

As always, any comments, suggestions would be most appreciated.

  David

> restart:
> # # # # # # # # # # # # # # # # # # # # # # # # # # # #

# Maple 7
> # Area puzzle involving squares & circles
> #To Do:  fill areas with color
> #  Use segment command and seq to make a set of colored lines
> #NB  Numbering for lines L1 is 1,2,3,4 for N,E,S,West
> #    Numbering for lines L2 is 1,2,4,3 for N,E,S,West
> # # # # # # # # # # # # # # # # # # # # # # # # # # # #
> with(plots):
> with(plottools):
> print(`The diagram shows two squares and two circles.`);
> print(`The red and green regions are equal in area.`);
> print(`To find the ratio of the radius of the large circle to the
> smaller.`);
> 
> #Doesn't seem to like a combination of geometry & with plots
> #with(geometry);
> r:=R*sqrt((4-Pi)/(Pi-2));  #for the pretty printout only!
> R:=49:
> r:=R*sqrt((4-Pi)/(Pi-2)):  #give r a numerical value
> c_big := circle([0,0], R, color=red):
> c_small := circle([0,0], r, color=green):
> sq_big := rectangle([-R,R], [R,-R], color=white):
> #sq_small := rectangle([-r/sqrt(2),r/sqrt(2)], [r/sqrt(2),-r/sqrt(2)],
> color=white):
> #y:=R/2:
> 
> SmallSq:=[]:
> for ii from 1 to round(r) do
> sq_small||ii := rectangle([-ii/sqrt(2),ii/sqrt(2)],
> [ii/sqrt(2),-ii/sqrt(2)], color=white,linestyle=1 , thickness=3):
> SmallSq:=[op(SmallSq),sq_small||ii]:
> end do:
> 
> Llines1:=[]:Llines2:=[]:Llines3:=[]:Llines4:=[]:
> for yy from 1 by 1 to R do
> l1||yy := line([-R,yy], [-sqrt(R^2-yy^2),yy], color=red, linestyle=1 ,
> thickness=3):
> l2||yy := line([sqrt(R^2-yy^2),yy], [R,yy], color=red, linestyle=1 ,
> thickness=3):
> l3||yy := line([sqrt(R^2-yy^2),-yy], [R,-yy], color=red, linestyle=1 ,
> thickness=3):
> l4||yy := line([-sqrt(R^2-yy^2),-yy], [-R,-yy], color=red, linestyle=1
> , thickness=3):
> #List of lines is Llines
> Llines1:=[op(Llines1),l1||yy]:
> Llines2:=[op(Llines2),l2||yy]:
> Llines3:=[op(Llines3),l3||yy]:
> Llines4:=[op(Llines4),l4||yy]:
> end do:
> first:=round(r*(sqrt(2))/2)+1:
> last:=round(r):
> L2lines1:=[]:L2lines2:=[]:L2lines2D:=[]:L2lines3:=[]:L2lines3Up:=[]:L2
> lines4:=[]:
> for yy from first by 1 to last do
> l2_1||yy := line([-sqrt(r^2-yy^2),yy], [sqrt(r^2-yy^2),yy],
> color=green, linestyle=1 , thickness=3):
> #l2_2||yy := line([yy,r/sqrt(2)],[yy,sqrt(r^2-yy^2)],  color=green,
> linestyle=1 , thickness=3):
> l2_2||yy := line([yy,sqrt(r^2-yy^2)],[yy,0],  color=green, linestyle=1
> , thickness=3):
> l2_2D||yy := line([yy,-sqrt(r^2-yy^2)],[yy,0],  color=green,
> linestyle=1 , thickness=3):
> 
> l2_3||yy := line([-yy,-sqrt(r^2-yy^2)],[-yy,0],  color=green,
> linestyle=1 , thickness=3):
> l2_3Up||yy := line([-yy,sqrt(r^2-yy^2)],[-yy,0],  color=green,
> linestyle=1 , thickness=3):
> 
> l2_4||yy := line([-sqrt(r^2-yy^2),-yy], [sqrt(r^2-yy^2),-yy],
> color=green, linestyle=1 , thickness=3):
> #List of lines is Llines
> L2lines1:=[op(L2lines1),l2_1||yy]:
> L2lines2:=[op(L2lines2),l2_2||yy]:
> L2lines2D:=[op(L2lines2D),l2_2D||yy]:
> L2lines3:=[op(L2lines3),l2_3||yy]:
> L2lines3Up:=[op(L2lines3Up),l2_3Up||yy]:
> L2lines4:=[op(L2lines4),l2_4||yy]:
> end do:
> 
> 
> plots[display](c_big,c_small,Llines1,Llines2,Llines3,L2lines1,L2lines2
> ,L2lines2D,Llines4, L2lines3,L2lines3Up,L2lines4,
> scaling=constrained);
> plots[display](c_big,c_small,Llines1,Llines2,Llines3,Llines4,L2lines1,
> L2lines2,L2lines2D,L2lines3,L2lines3Up,
> L2lines4,SmallSq,scaling=constrained);
> 
> 
Warning, the name changecoords has been redefined

Warning, the name arrow has been redefined

            The diagram shows two squares and two circles.

             The red and green regions are equal in area.

  To find the ratio of the radius of the large circle to the small\
        er.

                                     4 - Pi
                         r := R sqrt(------)
                                     Pi - 2
 

I'm a brand-new Maple user, so be gentle!

I was fooling around with a document and manually changed some fonts on various items, by just highlighting them and setting a new font.  I even selected everything and changed the font but not the size.  I didn't actually change any styles. 

I want to reset to the Maple default now, but can't seem to do it.  Format / Manage Style Sets... / Default Maple Style Set / OK doesn't do it, neither does Format / Manage Style Sets... / Load Style Set... navigating to the default stylesets\WorksheetDefault.mw and OK / OK.  Nothing seems to change.  I've been through Help:worksheet/documenting/styles and the verbiage doesn't match the dialog box screen shots there.  I'm not really sure what to do with that "help".

I can't seem to switch to a customized style set either.  If you manually change fonts, does that supercede the style?  Is there any way to revert?

Thanks for any help!

Hi,

I have a list of displayed sequences  

S[j]:=display(seq(R1[i],i= 1..ne),seq(R[i],i= 1..ne), scaling = constrained, axes = none);

that can be animated easily in a worksheet using the following command 

display(seq(S[n]$5, n=1..10), insequence=true);

but when I try to embed that in a maplet, it doesnt work. The problem is with insequence. I removed insequence and the maplet showed S[10]. What else can I use?  

What can I do to have the maplet show the sequence of displays? Is there a way to use the animate command here?

Thanks for the help. 

I'm trying to compute the flux over a closed cylinder but can't define the top and bottom.

For the envelope

works fine. But top and bottom?

why does the sum(sin(k), k = -214748364 .. 214748364) not equal 0?